Mathematics

Recommended readings

• Introduction to Linear Algrebra

• 3Blue1Brown

Syntax Guides

• https://github.com/cben/mathdown/wiki/math-in-markdown

• https://faculty.math.illinois.edu/~hildebr/tex/course/intro2.html

$$a^2 + b^2 = c^2$$

$$\alpha + \beta +\delta+\theta +\phi \rho$$

Consider (eq:a): $$ \alpha = \beta $$ (a)

Consider (eq:a):

$$ \alpha = \beta $$        (a)

$$@equation(id) x = \sum_{i=1}{N} i @/$$

@equation(id)
x = \sum_{i=1}{N} i
@/

$ y=\sum_{i=1}^n g(x_i) $

 $ y=\sum_{i=1}^n g(x_i) $

$$\begin{align} (a+b)^3 &= (a+b)^2(a+b)\\ &=(a^2+2ab+b^2)(a+b)\\ &=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\ &=a^3+3a^2b+3ab^2+b^3 \end{align}$$

\begin{align} 
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}

\[ \left|\sum_{i=1}^n a_ib_i\right| \le \left(\sum_{i=1}^n a_i^2\right)^{1/2} \left(\sum_{i=1}^n b_i^2\right)^{1/2} \]

\[
\left|\sum_{i=1}^n a_ib_i\right|
\le
\left(\sum_{i=1}^n a_i^2\right)^{1/2}
\left(\sum_{i=1}^n b_i^2\right)^{1/2}
\]